2017
Seismic design study of concentrically braced
frames with and without buckling-controlled
braces
Seyedbabak Momenzadeh
Iowa State University
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Recommended Citation
Momenzadeh, Seyedbabak, "Seismic design study of concentrically braced frames with and without buckling-controlled braces" (2017). Graduate Theses and Dissertations. 15579.
Seismic design study of concentrically braced frames with and without
buckling-controlled braces
by
Seyedbabak Momenzadeh
A dissertation submitted to the graduate faculty in partial fulfillment of the requirements for the degree of
DOCTOR OF PHILOSOPHY
Major: Civil Engineering (Structural Engineering)
Program of Study Committee: J. Jay Shen, Major Professor
Jon M. Rouse Behrouz Shafei Jeramy C. Ashlock
Alan Russell
Iowa State University Ames, Iowa
2017
DEDICATION
This study is dedicated to my mom and dad who have always been supportive even when I decided to pursue my education thousands of miles away from them. I could not have made any accomplishments if it was not for their endless sacrifices.
TABLE OF CONTENTS Page NOMENCLATURE ……… v ACKNOWLEDGEMENT ……….. vii ASBTRACT ……… viii CHAPTER 1. INTRODUCTION ………... 1 Background ………. 1 Motivation ………... 3
Problem Statements and Objectives ……… 6
Organization of the Dissertation ……….. 8
CHAPTER 2. LITERATURE REVIEW .……… 10
Introduction ………. 10
Experimental Tests on SCBFs ………. 11
Analytical Studies on SCBFs ……….. 17
Studies on Brace Ductility in SCBFs ……….. 19
Seismic Demand on Beams in SCBFs ………. 22
Seismic Demand on Columns in SCBFs ………. 23
Studies on All-Steel Buckling Restrained Braces ………... 28
CHAPTER 3. BUCKLING-CONTROLLED BRACES .……… 34
Introduction ………. 34
FEM-Based Evaluation of TinT-BCBs ………... 35
Testing of Round-in-Square BCBs ………. 51
Cyclic Behavior of CBFs incorporating BCBs ……… 55
Conclusions ………. 63
CHAPTER 4. SEISMIC BEHAVIOR OF SCBFs UNDER EARTHQUAKE GROUND MOTIONS ………... 65
Introduction ………. 65
Building Description ……… 66
Earthquake Ground Motion ………. 70
Effect of the Gusset Plates on the Behavior of Shear Connections ………. 71
Verification of RUAUMOKO-2D Model …….……….. 76
Frame Simulation Description ………. 85
Results of the Time History Analyses under GM11 ……… 87
Deformation of the Frame under Seismic Loads ………. 109
CHAPTER 5. SEISMIC BEHAVIOR OF BCBFs UNDER EARTHQUAKE GROUND
MOTIONS ……… 131
Introduction ………. 131
Modeling of BCBFs ………. 132
Seismic Response of SCBFs and BCBFs in Terms of SDR ……… 133
Seismic Response of SCBFs and BCBFs in Terms of Beam Behavior ………….. 135
Seismic Response of SCBFs and BCBFs in Terms of Column Behavior ………... 139
Seismic Response of SCBFs and BCBFs in Terms of Brace Ductility …………... 142
Effect of Bracing Configuration and Beam Strength on Seismic Response of BCBFs ………... 143
Conclusions ………. 147
CHAPTER 6. EFFECT OF LOADING PATTERN ON THE BEHAVIOR OF TSXBF ... 149
Frame Simulation ……… 149
Loading Patterns and Beam Sizes ………... 151
Summary of the Simulated Cases ……… 155
Results ………. 156
Conclusions ………. 173
CHAPTER 7. CONCLUSIONS AND RECOMMENDATIONS ……….. 175
General Remarks ………. 175
Conclusions ………. 176
Future Study ……… 178
REFERENCES ………...………. 180
APPENDIX A. TIME HISTORIES OF GROUND MOTIONS ………. 186
NOMENCLATURE
AISC American Institute of Steel Construction
ASTM American Society for Testing and Materials
BC Buckling Controller
BCB Buckling-Controlled Brace
BCBF Buckling-Controlled Braced Frame
BR Buckling-Restrainer
BRB Buckling-Restrained Brace
BRBF Buckling-Restrained Braced Frame
CBF Concentrically Braced Frame
CHS Circular Hollow Section
FE Finite Element
FEM Finite Element Method
FEMA Federal Emergency Management Agency
HSS Hollow Structural Section
MF Moment Frame
ODR Overall Drift Ratio
SCBF Special Concentrically Braced Frame
SDR Story Drift Ratio
SMRF Special Moment Resisting Frame
ACKNOWLEDGEMENTS
I would like to express my sincere gratitude to my adviser, Dr. Jay Shen, who provided me with the opportunity to join his research group and patiently advised me throughout all the stages of my Ph.D. research.
I also want to thank Dr. Onur Seker for mentoring me in my research. I am always grateful for his support and encouragement in various circumstances.
Special thanks to the faculty members who served on my committee: Dr. Rouse, Dr. Shafei, Dr. Ashlock, and Dr. Russel.
This research is partially supported by the American Institute of Steel Construction (AISC) and Iowa State University (ISU). The opinions expressed in this study are solely those of the author and do not necessarily reflect the views of AISC, ISU, or other agencies and individuals whose name appear in this document.
ABSTRACT
Special concentrically braced frames (SCBFs) have become more popular as lateral load resisting systems after disappointing performance of special moment resisting frames (SMRFs) in the 1994 Northridge earthquake. SCBFs dissipate earthquake energy through buckling of compressive braces and yielding of tensile braces. V-type, inverted V-type, and two-story X-bracing are three major categories of SCBF X-bracing configurations. According to the current design approach implemented in AISC 341-10, beams and columns in SCBFs shall be designed based on the capacity of the braces to keep the beams and columns in the elastic region. However, a limited number of studies have shown that braced-intersected girders in two-story X-braced frames do not always remain elastic during an earthquake, violating current design code assumptions. Inelastic behavior in girders is due to the unsymmetrical cyclic behavior of the braces that creates a considerable unbalanced force. In an attempt to achieve symmetrical behavior, buckling-restrained braces (BRBs) superior to conventional braces in terms of ductility and cyclic behavior have been developed, but the majority of the developed BRBs are relatively complex and costly, resulting in hesitancy in the engineering community to accept them as a proper substitute for conventional braces. The present study is intended to investigate whether SCBFs designed based on current design codes meet the current design codes requirements. A newly developed buckling-controlled brace (BCB) is also introduced and the effect of such braces on the seismic demand of SCBFs is studied. For this purpose, three SCBFs with different beam sizes and bracing configurations were designed in accordance with current design codes and a group of earthquake ground motions was applied to them to investigate their seismic responses. Conventional braces of these frames were also replaced with BCBs to evaluate the influence of the new developed
braces on the seismic response of the SCBFs. The results point out that girders and columns in TSXBFs yield under earthquake ground motions, while they are designed for the capacity of the braces and are expected to remain elastic. In addition, SCBF seismic demand is substantially reduced by replacing the conventional braces with BCBs, so it seems that BCBs would be a suitable substitute for conventional braces.
CHAPTER 1. INTRODUCTION
1.1. Background
Special moment resisting frames (SMRFs) were among popular lateral load resisting systems that had been broadly used before 1994, but severe damage observed after the 1994 Northridge earthquake and the 1995 Hyogo-ken Naubu (Kobe) earthquake caused the engineering society to be hesitant to use this type of system. After the discouraging SMRF performance, concentrically braced frames (CBFs) became more popular to engineers. Because of the more stringent requirements and restrictions now required for SMRFs, heavier beams and columns must be used in these systems, resulting in complex connection details and high labor costs. Conversely, special concentrically braced frames (SCBFs) are relatively easy to construct and cost-effective, making them advantageous over SMRFs. SCBFs are lateral load resisting systems that dissipate earthquake energy through buckling of compressive braces and yielding of tensile braces. V-type, inverted V-type (chevron) and X-type were three different bracing configurations that were commonly used in SCBFs, but X-type gradually became a rarely-used bracing type because of its additional connection costs. On the other hand, seismic design of brace-intersected girders in V-type and chevron frames usually led to deep girders that were also not desirable, so in an attempt to reduce girder size, engineers have been using two-story X-bracing systems that consist of V-type and inverted V-V-type bracing in alternating stories. As a result, V-V-type, inverted V-V-type and two-story X-bracing, shown in Figure 1, are the three major categories of bracing configuration currently used in SCBFs. During the past two decades, while extensive studies have been performed on the seismic behavior of the SCBFs, with the majority of these studies focused on the behavior of the braces, investigations regarding the beams and columns have been scattered and
scarce, even though study of the performance of braces, beams and columns that interrelate with one another as single systems seems necessary and important.
Figure 1: Typical Bracing configurations in SCBFs.
According to the AISC 341-10 [AISC, 2010], beams and columns must remain elastic during an earthquake. To fulfill this requirement, the demand in these members are calculated by three structural analysis cases, and the most critical one should be chosen for the design. Although it may have seemed sufficient to use current criteria to design the SCBFs, recent research has shown that a more thorough study is required to develop a better understanding regarding the demand in SCBFs [Uriz and Mahin, 2008].
1.2. Motivation
SCBFs have been widely used around the world, especially in the aftermath of the 1994 Northridge earthquake. Damages observed in such frames in past earthquakes, such as the 1985 Mexico [Osteraas and Krawinkler, 1989], the 1989 Loma Prieta [Kim and Goel, 1992], the 1994 Northridge [Tremblay, et al., 1995; Krawlinkler, et al., 1996] and the 1995 Hyogo-ken Naubu (Kobe) [AIJ/Kinki Branch Steel Committee, 1995; Hisatoku, 1995; Tremblay, et al., 1996], warned engineers to use caution in utilizing such systems. Figure 2 shows a fracture in a column that was initiated in the flange and developed further into the web during the Hyogo-ken Nanbu (Kobe) earthquake in 1995.
Figure 2: Column fracture in Hyogo-ken Nanbu (Kobe) earthquake (Tremblay et al., 1995).
To restore the confidence of engineers in using SCBFs, procedures specified in design codes have been changing over the past decades. According to the latest design code [AISC 341-10], braces should be designed as a “column” member to resist equivalent seismic forces calculated based on ASCE7-10. In addition, beams and columns must remain elastic and be designed based on the capacity of the braces. For this purpose, all tensile braces should be replaced by their expected tension capacity and all compression braces should be replaced by: 1) their expected buckling capacity; 2) their expected post-buckling capacity, as shown in Figure 3. The standard also states that braced frames must
be designed for the first mode loading pattern (Figure 4) and all tension and compression braces would reach their capacity simultaneously, even though recent studies have shown that this loading pattern is only one of the multiple possible patterns that might occur and the one chosen represents an optimistic case for frame design [Shen, et al., 2014]. In addition, according to AISC 341, even though designers are permitted to neglect the bending moment in the columns that should be designed under a compression force derived from structural analysis of the frame at the governed case, studies have demonstrated that flexural demand in columns caused by non-uniform story drifts [Koboevic and Redwood, 1997; Sabelli et al., 2003] would have a substantial effect on frame behavior and it is not safe for it to be neglected.
Figure 3: Three analysis cases. In Figure 3:
TET: Expected tensile capacity of the braces.
CEC: The smaller of {TET, 1.14×expected compression capacity of the braces}.
Figure 4: Anticipated braced frame mechanism (AISC341-16).
In summary, it seems that there are still some issues in SCBFs that should be addressed:
Previous experimental studies on SCBFs have shown that columns are susceptible to fracture at about 2.8% story drift ratio (SDR) [Uriz, 2005; Uriz and Mahin, 2008]. This is an issue of special concern because of the fact that columns are the most important members in a frame. The premature fracture described earlier was mainly due to the shortage of knowledge regarding the column demands.
Although extensive research has been carried out on inelastic behavior of steel braces, the effect of brace performance on column demand is still unclear. It is also worth mentioning that braces in different configuration have different effects on column demand. Since the evaluation of these effects is missing in the current literature, this study aims to cover these issues.
While researchers have previously used pin beam-to-column connections in their simulations for studying the behavior of braced frames, the rigidity of these connections have a direct impact on the bending moment transferred from beam to column, so the connection type will have a significant effect on the column demand and there is a need to evaluate whether or not the pin connection assumption is sufficiently accurate.
In addition to the above issues, despite the fact that engineers believed that the bending moment in the columns in SCBFs is negligible, premature column fracture in recent experimental studies have demonstrated that there is a considerable demand (flexural and axial) on the columns, especially after 1% SDR. Although empirical methods have been proposed to estimate flexural demands in columns in SCBFs [MacRae, et al., 2004], the relationship between the flexural demand on the column and brace behavior is still only vaguely known.
In conclusion, all the previously mentioned issues clearly indicate the necessity of a thorough study on the seismic demand of SCBFs.
1.3. Problem Statement and Objectives
Extensive and unexpected damages observed in various experimental studies [Uriz and Mahin, 2008; Lai and Mahin, 2010] demonstrate that, while SCBFs are useful as lateral load resisting systems, there are some inconsistencies in current design methods that may lead to severe damage to the frames. As mentioned earlier, various analysis cases required by AISC for designing SCBFs show that there are some issues in predicting the actual required axial force in the column
(Pr) and amendment to this provision seems inevitable. Moreover, substantial flexural demand on
columns in SCBFs can result in their early fracture [Uriz and Mahin, 2008], mainly because of premature fracture of the braces and framing action that in turn may produce a substantial demand on the columns. The aforementioned complex behavior and tedious design procedures are mainly because of difficult to predict nonlinear behavior of the buckled braces.
Use of buckling-restrained braces (BRBs) has become popular among the engineers in recent years, mainly because of the large hysteretic loops exhibited by BRBs when compared with conventional braces. Buckling-controlled braces (BCBs) that perform similar to BRBs are bracing members newly-developed by the current research group. Preliminary analyses of BCBs have shown that they can be an effective substitute for conventional braces because of their stable and symmetrical cyclic behavior and cost-effectiveness. Although inelastic cyclic behavior of the isolated brace specimens has been experimentally and numerically studied, there remains a need for comparing the seismic demand of BCBFs with that of SCBFs, so there is a need to assess the influence of BCBs on the demand on the members used in SCBFs. In summary, the objectives of the present study are to:
Assess the reliability of current design procedure for SCBFs and make recommendations for improving frame performance.
Investigate the behavior of BCBs under different loading types to study the impact of different parameters on the overall response of the braces.
Study the effect of the brace section on BCB performance.
Assess the effect of beam strength and bracing configuration on the demands on members of SCBFs.
Investigate the effect of incorporating the newly-developed BCBs on the seismic behavior of SCBFs.
1.4. Organization of the Dissertation
Chapter 2 provides an extensive literature survey related to (1) experimental tests on SCBFs; (2) analytical studies on SCBFs; (3) experimental and analytical studies on single isolated braces and brace ductility in SCBFs; (4) seismic demand on beams in SCBFs; (5) seismic demand on columns in SCBFs; and (6) experimental and analytical studies on buckling restrained braces and an introduction to buckling-controlled braces.
Chapter 3 presents an introduction to BCBs and effect of using different cross sections on the behavior of braces is assessed under both monotonic and cyclic loading. In addition, impact of the BCBs on the behavior of the SCBFs is studied through finite-element simulations.
Chapter 4 presents seismic response of a 9-story steel braced frame under twenty earthquake ground motions. Three different bracing configurations are studied and their performance is compared in terms of brace ductility and beam and column seismic demand. Moreover, influence of the strength of the brace-intersected beams on the seismic response of the SCBFs is investigated.
Chapter 5 presents the seismic response of SCBFs incorporating BCBs. Seismic behavior of a 9-story BCB-frame is compared with a conventional frame and effect of beam strength on BCBF response is evaluated using nonlinear dynamic analyses.
Chapter 6 presents the impact of the different loading patterns on the behavior of SCBFs. Four different loading patterns are extracted from the deformation of the 9-story frame simulated
in Chapter 4. The loading patterns are applied to a two-story X-braced frame and the beam and column response is studied through extensive finite-element simulations.
Chapter 7 summarizes the results obtained in this investigation and provides important conclusions. Recommendations for future studies related to the seismic behavior of steel braced frames are also discussed.
CHAPTER 2. LITERATURE REVIEW
2.1. Introduction
SCBFs have been among the most interesting lateral load resisting systems studied by structural researchers over the past two decades. Braced frames currently comprise about 40 percent of the buildings in California and the trend for their use is believed to be increasing [Chen, 2010]. Extensive experimental and analytical studies have been conducted on the performance of the braces [Tremblay, 2002; Lee and Bruneau, 2005; Yang and Mahin, 2005, Tremblay, et al., 2008, Fell, et al., 2009, Nip, et al., 2010], gusset plates [Roeder, et al., 2006; Chambers and Ernst, 2005, Roeder, et al., 2010] and frames [Khatib, et al., 1987; Tremblay, et al., 1995; Sabelli, 2000; Sabelli and Mahin, 2003; Tremblay, et al., 2003, Uriz and Mahin, 2008, Shen et al., 2014; Shen et al., 2015]. In this chapter, previous studies related to the present investigation are reviewed and necessary comments are made regarding these results. This chapter can be divided into five sections:
i. Studies on experimental tests on SCBFs. ii. Analytical studies on SCBFs.
iii. Experimental and analytical studies of single braces and brace ductility in SCBFs. iv. Seismic demand on beams in SCBFs.
v. Seismic demand on columns in SCBFs.
2.2. Experimental tests on SCBFs
2.2.1. Experimental Test Carried out by Uriz and Mahin in 2008 at UC-Berkeley
A full-scale test on a chevron frame was carried out in 2001 by Uriz and Mahin at UC Berkeley. That test can be considered to be the starting point of an era in which researchers realized that full-scale tests were required for enhancing our knowledge regarding the behavior of structures, with this frame being one of the first tested full-scale steel frames. The frame was designed based on the AISC seismic provision 1997 and was comprised of two 9 ft stories and one 20 ft bay with chevron bracing in both of stories. Cyclic loading was applied to the roof through a loading beam as shown in Figure 5.
a) Elevation of the Tested Frame b) Loading Protocol Figure 5: Tested frame by Uriz and Mahin (2008).
The key observations of this study can be summarized as follows:
The first story braces began out-of-plane buckling at 0.67% overall drift ratio (ODR) and the deformation of the frame was concentrated in the first story, while the second story of the frame remained almost un-deformed. The ODR can be calculated by dividing the roof displacement of the frame-by-frame height.
An early brace fracture occurred at 1.35% ODR, as can be seen in Figure 6 and, as a consequence, beams and columns contributed to resisting the applied load, leading to column fracture as well.
It should be mentioned that the column used in this frame satisfies the requirements of the current design code (based on the calculations of the author) and the early fracture in the column (Figure 6) was mainly due to the unpredicted large demand on the column.
a) Fracture in the brace at 1.35% ODR b) Fracture in column at 1.35% ODR Figure 6: Fracture at 1.35% ODR in Uriz and Mahin test (2008).
Figure 7: Deformation of the frame at the end of the test (Uriz and Mahin 2008).
2.2.2. Experimental Test Carried out by Lai and Mahin in 2013 at UC-Berkeley
A full-scale test on an SCBF was performed in 2013 in the UC-Berkeley laboratory by Lai and Mahin. A two-story steel frame with one bay was tested for four different brace sections, the first two of which are of interest in this study. The frame was constructed with a story height of 9 ft and a 20 ft spacing between columns. V-type braces were employed in the first story of the frames and inverted V-type braces were used for the second story. A linear lateral force was applied at the floor levels of the frame using two actuators at each level. Figure 8 shows the second specimen constructed in the lab.
Figure 8: Test specimen constructed in UC-Berkeley by Lai and Mahin in 2013. The frame was designed according to the AISC seismic provisions [AISC 2005b] and ASCE-7 [2005]. Table 1 provides the member sizes used in this investigation.
Table 1: Member sizes used in experimental study by Lai and Mahin in 2013.
First Story Second Story
Columns Beam Braces Columns Beam Braces
Specimen 1 W12x96 W24x68 HSS6x6x3/8 W12x96 W24x117 HSS5x5x5/16 Specimen 2 W12x96 W24x68 HSS6x0.5 W12x96 W24x117 HSS5x0.5
The experimental process was divided into several sets of loading steps, each consisting of two complete cycles except for the first loading step that had six complete cycles. Details of the loading sequence are presented in Figure 9.
Figure 9: Loading sequence used in an experimental test by Lai and Mahin in 2013. The key observations of this study can be summarized as follows:
Braces in both of the specimens experienced out-of-plane global buckling in both stories at about 0.5% ODR.
Local buckling at the end of the first story beam in both specimens was observed at 1.4% ODR, as can be seen in Figure 10a. It is worth mentioning that each beam in both of the stories in the tested specimens were required to be designed as a beam-column member in conformance with AISC 341-10, while neither beam used in these frames satisfied the compressive member compactness requirement defined by AISC341-10. The early local buckling in the beams could have been avoided if proper sections had been used.
Square braces in the first story of the first specimen fractured at 1.9% ODR (Figure 10b), while no cracks were observed in the round braces used in the second specimen. It should be noted that, although the braces were properly working at this stage, the first-story beam in specimen 2 fractured at this drift value (Figure 10c). These results might have produced a major concern to the researchers because other studies have shown that drift demand in
the SCBFs might exceed even 4% with a 2% probability of exceedance in 50 years [Uriz 2005, McCormick et al. 2007].
Columns in both of the specimens yielded at 1.4% ODR, with yielding in the top portion of the columns in specimen 1 and a vertical yielding line in the column in specimen 2 observed. Figure 11 presents the P-M interaction curves of the columns in the tested frames that clearly demonstrate that the columns yielded during the test. This is an important result for the current study because, as mentioned earlier, columns are required to remain elastic and should not experience any yielding during the earthquake. It seems that the seismic demand on the columns in SCBFs is somewhat underestimated in the current design code.
Figure 10: Test results provided by Lai and Mahin (2013).
Figure 11: Column results provided by Lai and Mahin (2013). a) Local Buckling in top flange b) Brace Fracture
Flange c) Beam Fracture Flange a) P-M Interaction in 1st Spec. Flange b) P-M Interaction in 2nd Spec. Flange c)
2.3. Analytical studies on SCBFs
Shen, et al., (2015) carried out numerous dynamic time history analyses and finite-element based simulations to investigate the behavior of two-story X-braced frames. 6- and 12-story buildings were simulated in RUAUMOKO and 20 ground motions were applied to the frames. A two story X-braced frame was then simulated in ABAQUS. Based on their results, the following conclusions were drawn:
The first-mode mechanism is an optimistic case to occur in the two-story X-braced frames, and it leads to design of shallow beams for braced-intersected beams, even though the current design code clearly states that SCBFs should be designed based on the first mode deformation, a recommendation that seems insufficient. Deformation of the simulated frame a under first-mode loading pattern is presented in Figure 12, and severe deformation in the second-story beam can be observed in this figure.
Figure 12: Deformation of the frame under first-mode loading pattern at 4% 1st SDR (Shen et al. 2015).
Large inelastic vertical deflection occurs in the brace-intersected beams after the beam yields, inducing additional demand in the braces and connections. Because pin
connection performance in actual structures closely resembles that of rigid connections, it can be assumed that the additional demand in the connections will be transferred to the columns as well.
Kumar, et al., (2017) performed dynamic analysis in Perform-3D to study the seismic response of steel braced frames and they consequently proposed a new design approach taking into account the flexural demand on columns. They proposed three different limit states (P1 through
P3) for braced-frame design, but it seems difficult to utilize this design approach in practice. In the
first limit state, the frame should be designed according to the current design code and based on the member sections, critical axial force, and bending moment of each member can be achieved. Then, as a second try, based on the calculated forces, new sections would be designed. This method can be so time-consuming and it may need several attempts before the convergence is reached. In the third limit state, it is assumed that two plastic hinges will form at the top and bottom of each column and the columns would be designed based on their flexural capacity. Although this approach might be useful for lower stories in high-rise buildings, there is not sufficient information in that paper to determine how many stories should be designed based on this approach. It is obvious that this method will lead to over-designed sections in the top stories and that design will be too conservative. Another shortcoming of that study could be the sections used for the columns, with the proposed method leading to heavy sections such as W40×397, not practical for use in real structures. It therefore seems that a comprehensive research study is required to determine the demand on the columns in SCBFs and compensate for the aforementioned shortcomings.
2.4. Studies on brace ductility in SCBFs
Various studies have investigated the behavior of single braces under cyclic loading. Nip, et al., (2010) carried out an experimental test on 16 small HSS sections (HSS40x40 mm2 and HSS60x60 mm2). Based on the section size and length, brace ductilities varying from 4 to 10 were
achieved in the test. Figure 13a shows the result of a test on the specimen for which the ductility was around 10. Brace ductility can be calculated by dividing the maximum axial displacement of the brace prior to fracture by the yielding displacement. It should be noted that brace ductility depends on different parameters such as section size, specimen length, etc. Regarding the fact that larger sections are usually used in real structures, the calculated ductility might not be applicable to practical cases. In an attempt to investigate the behavior of a more practical section, Fell, et al., (2009) performed an experimental test on eighteen braces in which seven cases out of eighteen were conventional HSS sections. They tested HSS4x4 sections that were still smaller than the braces usually used in the steel structures, but the slenderness ratio was roughly 77, close to that of the real braces. All the braces fractured at about 2.5% SDR (Figure 13b), similar to the test results provided by Uriz and Mahin (2008) and Lai and Mahin (2010).
a) Nip et al. test (2010).
b) Fell et al test (2009).
In 2008, an experimental test by Tremblay, et al., was performed on isolated single specimens in the Hydro-Quebed structural engineering laboratory at Ecole Polytechnique of Montreal. (2008). The importance of this study can be summarized in two observations: 1) they used large sections like those commonly used in steel structures; 2) unsymmetrical gusset plates were used in the test to reflect the authentic behavior of braces in a frame. Three rectangular hollow sections (RHS) and two circular hollow sections (CHS) were tested in this study and the following conclusions were made:
The maximum SDR reached by the specimens were about 2%, as shown in Figure 14.
By decreasing the width-to-thickness ratio of the section, fracture in the braces can be postponed.
Both RHS and CHS specimens fractured before reaching the current SDR demand described in various studies [Uriz 2005, McCormick et al. 2007].
Figure 14: Specimens tested by Tremblay et al. (2008).
Table 2 summarizes the results of the studies related to peak brace ductility. As can be seen in this table, the maximum ductility capacity of HSS sections is about 10.
Table 2: Peak brace ductilities of the recently tested tubular bracings.
Item Test ID Brace Member (mm × mm × mm) b/t or D/t KL/r Peak Brace Ductility (µ)* Reference 1 S85-14 HSS100×100×6 13.7 85 10.00 Han et al. (2007) 2 HSS1-1 HSS102×102×6.4 14.2 77 8.90 Fell et al. (2009) 3 3B HSS127×127×8.0 15.0 65 6.00 Shaback and Brown
(2003) 4 2B HSS152×152×9.5 12.1 52 7.00 5 RHS19 HSS254×254×15 14.2 60 8.00 Tremblay et al. (2008) 6 RHS2 HSS254×254×15 14.2 40 6.00 7 CHS2 HSS273×9.5 30.8 62 10.00 8 CHS1 HSS273×9.5 30.8 42 8.50 9 2050-CS-HR HSS40×40×3 13.3 135 10.00 Nip et al. (2010) *The given ductility ratios are estimated from the published plots.
2.5. Seismic demand on beams in SCBFs
Shen, et al., (2014) simulated six SCBFs in RUAUMOKO-2D to investigate seismic demand on brace-intersected beams. A 6- and a 12-story frame were simulated with two different types of bracing configurations (Two-story X-bracing (TSXBF) and chevron) to compare the beam demand in different types of frames. In addition, two different design approaches were used for each TSXBF, producing both a strong and a weak brace-intersected beam. The latter was designed based on current design codes and the former designed similarly to chevron frames. Incremental dynamic analyses (IDA) were performed on each frame under ten pairs of ground motions and the intensity of the ground motions were increased until peak SDR in the frame reached 6%. Key observations of that study can be summarized as follows:
Brace ductility increases substantially after brace-intersected beam yielding in weak beam frames, mainly due to the vertical displacement of the beam, as can be seen in Figure 15.
SDR, used in the current design code to represent the seismic response of a structure, is not a proper index to be used in SCBFs. With respect to the vertical displacement of the yielded braced-intersected beam, brace ductility demand increases dramatically and could be close to the fracture point even for an SDR smaller than 2%, as can be seen in Figure 16a and Figure 16b. When Sa is equal to 1.5 in the weak beam frame (type B),
Figure 15: Deformation of the 12-story frame type B [Shen et al. 2014].
i. Sa[T1] vs. SDR ii. Sa[T1] vs. Brace ductility demand
Figure 16: Seismic response of 12-story frame [Shen et al. 2014]. 2.6. Seismic demand on columns in SCBFs
Flexural demand on the columns in SCBFs is predominantly due to the non-uniform SDR along the height of the frame [Sabelli, et al., 2003]. The change in the SDRs in alternate stories represents the need for the column to bend. Although the SDR in the frames can be readily calculated, a method for relating the SDR to the flexural demand on the columns remains vague. In an attempt to resolve this issue, MacRae, et al., (2004) proposed an empirical formula shown as
Equation 1 to take into account the effect of the SDR on the bending moment demand on the columns. 𝑀𝑐,𝑚𝑎𝑥 = 𝑀𝑐,𝑚𝑒𝑐ℎ( ∆𝑡 ∆𝑡𝑚) 0.65 ≤ 𝑀 𝑐,𝑚𝑒𝑐ℎ Equation 1
In the above formula:
Mc,max=Maximum column moment;
Mc,mech=Maximum column moment in the frame at mechanism formation;
Δt=roof displacement;
Δtm=roof displacement at mechanism formation.
Although the above formula can be a helpful step towards implementing the flexural demand in the design process, there are some issues of concern in this study that must be considered. Although most of the results presented in this paper (including the above formula) are derived based on a drift concentration factor (DCF) defined in the study, it seems that DCF is not a proper index to be used for evaluation of the braced frame response. Although different parameters such as brace ductility help us to understand at what stage the structure is, DCF does not seem to be helpful. It also seems clear that any approach for designing the columns should include performance of the braces, so this formula can be valid only if the braces do not fracture. All of these limitations show that a new approach for solving the column design issue is still needed.
Newell and Uang (2006) conducted an experimental and numerical study to investigate seismic demand on steel columns. Their study was done in three phases. In the first phase, they applied twenty ground motions to simulated columns using DRAIN 2DX and, based on the story drift time histories of columns, they developed a loading sequence for their experimental test; the proposed loading protocol is presented in Figure 17. In the second phase, they conducted an
experimental test and applied the proposed loading protocol to the steel columns in the University of California San Diego laboratory. In the third phase, they simulated the tested columns in ABAQUS and verified their simulation with the test results. Their simulation results led to the conclusion that steel columns experience yielding as seen in Figure 18, that shows the result for one of the columns under three different axial load ratios. This result demonstrated once again that current design provisions cannot be met by steel columns during an earthquake, and some design modifications are necessary.
Figure 17 : Loading sequence developed by Newell and Uang (2006).
a) 35% Py b) 55% Py c) 75% Py
Figure 18: P-M interaction in columns [Newell and Uang 2006].
Recently, Richards (2009) used RUAUMOKO-2D to investigate the seismic demand on columns in special braced frames. He simulated 36 frames with three different heights (3-, 9- and
18 stories), three different bracing types (BRBFs, SCBFs, eccentrically braced frames (EBFs)) and four different strength levels for each frame. He concluded that column axial demand in the upper stories of tall braced frames could be more than two times higher than those commonly used in the design, and maximum column axial demand at the base of the 9- and 18-story BRBFs and EBFs were only 55-70% of the demand commonly used in design. In addition, the study stated that braces do not reach their capacities in tension and compression at the same time, so the mechanism suggested by current design code is unlikely to happen. Although some of these conclusions might be correct, there are certain issues that cast doubt on the accuracy of the results, including:
Based on the current design code, brace-intersected beams should be designed for gravity loads as “beam” members, while beams in the other stories should be designed for both gravity and seismic loads as “beam-column” members, so it seems that different beam sizes should be used for alternate stories, even though identical beam sections were used for all the stories in this study.
W16x40 is used for the beams in even stories, even though it is not a compact section and is prohibited for uses in “beam-column” members, so it seems that beams were not properly designed in the study.
Effects of the bending moment on column demand is neglected in this study even though they make a major contribution in the column demand and might affect the conclusions.
In 2010, Chen carried out several numerical analyses to assess the seismic demand of SCBFs. He simulated three SCBFs and three BRBFs with different heights using OpenSees (the Open System for Earthquake Engineering Simulation) and applied a suite of ground motions to the frames, and P-M interaction of the first story columns in each frame is presented in Figure 19.
As can be seen in the top row, almost all the columns in the SCBFs experienced yielding. In addition, interaction curves in the bottom row which representing the BRBFs prove that they performed slightly better than conventional frames but they are also still close to yielding [Chen, 2010]. With respect to the data provided, the following comments can be made on the results:
Yielding patterns in the 3- and 6-story SCBFs were similar to one another with flexural demand predominant in these cases. However, in the 16-story frame the yielding pattern completely changes and the axial force ratio is dominant in this case. This phenomenon can be explained by taking into account the effect of the higher mode deformation that can produce the maximum axial force in the column while the bending moment is small. In the shorter frames this effect is negligible and flexural demand has the major contribution in the demand on the columns.
The behavior of TSXBF was evaluated in this study and there remains a need to assess the applicability of the provided result to the chevron frames, another common bracing configuration in steel structures.
2.7. Studies on all-steel buckling restrained braces
While Hollow Structural Sections (HSS) are the most popular shapes utilized in Special Concentrically Braced Frames (SCBFs) construction because of their large strength-to-weight ratios and construction simplicity, premature failure potential and unsymmetrical hysteretic behavior of such braces may trigger non-uniform distribution of the plastic deformations (vertically and horizontally), as well as negatively affecting ductile (special) CBFs in terms of overall energy dissipation capability.
A ductile CBF dissipates the major portion of the seismic energy input through buckling and yielding of braces that would undergo large ductility demands, on the order of 10 to 25 [Shen, et al., 2014 and 2017], when subjected to severe earthquake ground motions, as shown in Figure 20.
Figure 20: Brace ductility demand under different ground motions [Shen et al. 2017]. Several evaluations of seismic demands in ductile CBFs [Uriz, 2005; Sabelli and Chunho, 2001; McCormick, et al., 2007] indicated that mean peak inter-story drift demands on CBFs may
reach nearly 4% [Sabelli, et al., 2007] and perhaps even up up to 5.7% [Uriz, 2005]. Recent experimental studies [Uriz and Mahin, 2008; Park, et al., 2004; Nip, et al., 2010; Fell, et al., 2009; Shaback and Brown, 2003; Goggins, et al., 2006; and Tremblay, et al., 2008], on the other hand, have shown that a few cycles with relatively large plastic amplitudes can lead to local buckling-induced fracture in HSS braces, possibly in turn precipitating torsional irregularities and inelastic deformations (or even fracture) in columns [Uriz and Mahin, 2008] due to framing action subsequent to brace fracture, as it can be seen in Figure 21.
Figure 21: Column fracture subsequent to brace fracture [Uriz and Mahin, 2008]. Moreover, as mentioned in the previous chapters, experimental studies on isolated steel brace specimens have demonstrated that brace fracture is likely to occur prior to attaining a peak brace ductility of 6 [Shaback and Brown, 2009; Tremblay, et al., 2008] to 10 [Tremblay, et al., 2008; Han, et al., 2007], corresponding to an equivalent inter-story drift angle of 0.015 to 0.025. This large discrepancy between the anticipated ductility capacity of ductile CBFs and the seismic demand on the structure may be attributable to early experimental data obtained from testing of small-size conventional braces made of double angles [Jain, et al., 1987; Black and Wegner, 1980; Astaneh Asl, et al., 1985], double channels [Black and Wegner, 1980], W- and WT-shapes [Black
and Wegner, 1980; Leowardi and Walpole. 1996], that usually exhibit longer fracture life than tubular braces.
Furthermore, conventional buckling braces exhibit unstable and unsymmetrical inelastic cyclic behavior due to strength degradation following brace buckling. This abrupt change in compressive strength not only imposes large unbalanced brace forces [Tremblay and Nobert, 2000] on brace-intersected girders and columns in braced bays, but also significantly amplifies the possibility of weak story formation [Sabelli, et al., 2003] in conventional CBFs. Although recent advances in seismic design provisions [i.e., AISC 341-10 and Eurocode 8 (EC8)] have resulted in more stringent design requirements for ductile CBFs with the purpose of enhancing their relatively lesser ductile behavior, researchers have addressed issues associated with non-dissipative structural member design, which are designed to remain elastic, such as girders [Shen, et al., 2014 and 2015] and columns [Brandonisio, et al., 2012; Marino 2014] in ductile CBFs. For example, Brandonisio, et al., (2012) proposed an alternative approach to the one stipulated in EC8 in which the authors modified the over-strength factor and slenderness limitations given by EC8 to reduce the overall structural weight and obtain a more uniform plastic deformation distribution along with satisfactory overall nonlinear behavior. Similarly, Bosco, et al., (2014) studied the seismic response of columns in 4- and 8-story CBFs with diagonal braces by means of non-linear dynamic analyses using five sets of ground motions. Their results indicated that both gravity columns and columns in braced bays designed according to EC8 experienced yielding (or buckling) before diagonal braces attained their assumed ductility limits.
Efforts to mitigate seismic hazards in CBFs have resulted in numerous concrete-encased and all-steel buckling restrained braces (BRBs) [Zhao, et al., 2011; Usami, et al., 2011; Ma, et al., 2011; Razavi, et al., 2012; Clark, et al. 1999]. All-steel BRBs are comprised of a steel core that
carries the applied load and a restraining system that prevents buckling of the main core. Although all-steel BRBs have been increasingly attracting more attention from researchers, the extreme complexity [Zhao, et al., 2011; Usami, et al., 2011] of all-steel BRB configurations are among the drawbacks of such braces (Figure 23), making the engineering community hesitant to employ them as an effective substitute for conventional steel braces in an actual CBF construction.
Figure 22: Assembly and hysteretic behavior of a typical concrete-encased BRB (Clark et al. 1999).
a) All-steel BRB configuration (Zhao et al. 2011)
b) All-steel BRB assembly (Ma et al. 2011)
Figure 23: Complex assembly of conventional all-steel BRBs.
For the purpose of avoiding such complexity, instead of using a combination of filler plates, channels, and HSS along with bolted or welded attachments as a buckling restraining mechanism,
Shen, et al., (2017) introduced a simple and promising buckling-control concept without compromising the intended performance goals and practicality. As illustrated in Figure 24, a Tube-in-Tube buckling-controlled brace (TinT-BCBs) consists of a load-bearing tube (main brace) providing resistance to seismic forces, encased in another tube (controlling section) of circular or rectangular HSS that controls both global and local buckling of the main brace by providing continuous lateral support along the brace length. Note that the gap between the tubes is provided to limit the contribution of the outer tube to the axial load-carrying system. A FEM-based numerical study performed by Shen, et al., (2017) has discussed the influential parameters, i.e., the gap between the tubes, the relative outer tube thickness and the coefficient of friction, using built-up HSS with square-in-square bracing configuration to establish a conceptual foundation for cyclic behavior of TinT-BCBs. Their study implied that TinT-BCBs are promising both in terms of economy and in overcoming the aforementioned issues related to seismic performance of ductile braced frames.
a) Square-in-round b) Round-in-square
Figure 24: Scheme of TinT-BCBs.
In summary, while various studies have either experimentally or numerically investigated the behavior of the SCBFs, there are still some gaps in the current literature that should be addressed. Some of the major missing parts are as follows:
It is still difficult to understand the relationship between the bending moment demands on the columns and brace ductility in SCBFs.
It is important to understand how different bending moment in the column could be achieved by changing the bracing configurations in the braced frames.
It is necessary to evaluate the rigidity of the beam-to-column connections and assess its impact on the flexural demand on the members.
It seems important to study the effect of the variation in cross-section on the performance of the BCBs.
The effect of the BCBs on seismic demand of SCBFs with different bracing configuration should be investigated.
CHAPTER 3. BUCKLING-CONTROLLED BRACES
3.1. Introduction
While Special Concentrically Braced Frames (SCBFs) are widely used globally in earthquake resisting systems because of their simplicity in construction and design, premature brace failure in CBFs is one of the main issues of such system and researchers have been trying to find a solution to this problem. In an attempt to overcome this issue, engineers have developed buckling-restrained braces (BRBs) to increase the ductility of the braces and to postpone fractures. BRBs are composed of a structural steel cores that bear the loads and a system that restrains the steel core from buckling [AISC 341-10]. All-steel and concrete-encased BRBs are two different types of BRBs that have been developed in recent years. Various configurations for all-steel BRBs [Zhao et al., 2011; Usami, et al., 2011; Ma, et al., 2012; and Razavi, et al., 2012] and concrete-encased BRBs [Tremblay, et al., 2006; Park, et al., 2009; Lin, et al., 2012] have been developed to effectively restrain the buckling of braces and reach stable and symmetrical hysteretic behavior. Although performance of BRBs is considerably superior to that of conventional braces, there are still some issues that make the engineering community hesitant to accept them as an effective replacement for conventional steel braces. For example, among the drawbacks of these braces are the complex and expensive configurations of some of the developed BRBs. In addition, compression strength adjustment factor, calculated by dividing the compressive strength by tensile strength, can be as large as 1.5 in some of the BRBs [Palmer, et al. 2014], and this difference can lead to significant unbalanced forces in CBFs, so it seems that there is a need to develop a new brace that not only exhibits symmetrical hysteretic behavior but also is cost-effective and easy to
construct. To address this issue, a new all-steel buckling-controlled brace (BCB) has been developed in the present study.
This chapter investigates the relative effectiveness of TinT-BCBs with Round-in-Square and Square-in-Round configurations with an emphasis on the efficiency and applicability of the developed TinT-BCBs composed of HSS that can be employed in an actual CBF construction. The results are evaluated in terms of hysteretic response of bracings and global response of braced frames both with and without a buckling-controller by means of both testing and Finite-Element (FE) simulations. For this purpose, the behavior of a set of isolated TinT-BCBs with round-in-square and round-in-square-in-round configurations was first compared through FE simulations under uniaxial and cyclic loading. Subsequently, response of the braced frames that incorporate conventional braces and TinT-BCBs are compared with respect to plastic deformation distribution on structure, braces, and girders. Finally, two round-in-square type BCB specimens have been tested to validate the observations carried out in the model-based study.
3.2. FEM-based evaluation of TinT-BCBs
A FEM-based parametric study was performed on several BCBs with different sections, gap sizes, and friction coefficients to evaluate the comparative efficiency of round-in-square and square-in-round TinT-BCBs. The general scheme of the simulations described in this chapter can be summarized as follows:
i. Investigating the behavior of isolated BCBs under monotonic compression. ii. Examining the influence of connection design on the behavior of BCBs. iii. Studying the cyclic behavior of the developed BCB.
3.2.1. Isolated BCBs under monotonic compression
In the first phase of the model-based study, an ensemble of isolated TinT-BCBs with round-in-square (RS) and square-in-round (SR) configurations were subjected to monotonic loading to better comprehend and assess the influence of each configuration (RS and SR). Table 3 summarizes influential design parameters, i.e., the ratio of the outside tube thickness to the main tube’s, the coefficient of friction between the outer surface of the inside tube (main brace) the inner surface of the outer tube (buckling-controller), and the initial gap between the tubes. As illustrated in Figure 24, the initial gap is defined as the minimum distance between the inner and outer tubes.
The gap amplitudes varied from a small gap of 0.017” to a relatively large gap of 0.1765”. Two different friction coefficients were considered for each main brace-buckling controller couple (Table 3). Friction coefficients of 0.3 and 0.1 were selected to represent bare steel and lubricated steel surfaces, respectively. Simulation cases were divided into SR and RS groups, , based on their cross-sectional configurations. As given in Table 3, SR group represents BCBs with a square load-bearing tube encased in a round outer tube, while the RS group included models comprised of a round inside tube and a square outer tube. In addition to the TinT-BCB models, for the sake of the comparison, a conventional brace simulation was also performed for each simulation group (SR and RS). Note that the main brace (load-bearing tube) section was identical for all models in the same simulation group.
All models were analyzed using a general-purpose finite-element software package, ABAQUS (Hibbit et, al., 2001). Values of modulus of elasticity and Poison’s ratio were assumed to be 29,000 ksi and 0.3, respectively. Nominal material properties with kinematic hardening rules were used for non-linear material definition of all models.
Table 4 shows the material properties adopted for the simulation cases. Since initial imperfections could have a substantial impact on the buckling load and hysteretic behavior, a two-step analysis was conducted on each model to properly represent initial deflections. In the first step, an elastic buckling analysis was conducted to obtain the buckling modes of each model. Subsequent to the buckling analysis, an imperfection of 1/1,000 of the brace length was applied to the models, considering the first buckling mode of the member. In the second step, a large-displacement static analysis was carried out to analyze each model under compression force. This approach allowed the static analyses to begin from a zero-stress condition. The dissipated energy fraction was set to 2e-4 in the automatic stabilization method to lessen convergence problems during the analyses. A full Newton method was utilized as the solution technique and geometric nonlinearities were taken into account in the analyses. A 3D 8-node linear brick element with reduced integration was employed to mesh the members (C3D8R). Care was taken in the modeling of the contact elements.
A hard contact method was used for the interactions normal to the surfaces to prevent any penetration, while the penalty method was used to describe friction formulation for the tangential interaction between inner and outer tubes. A fixed boundary condition was applied to one end, while relative axial displacements were applied from the other end of the specimens. A mesh size of 0.5 inches was used along the main brace length except for the locations that are expected to experience local deformations. A finer mesh was employed in critical sections like the mid-length of the conventional bracing. Two elements were also defined in the thickness of the gusset plates, inner, and outer tubes to properly capture the anticipated local deformations. Figure 25 shows the meshing for the one of the cases. Small circles and squares next to each member represent number of nodes and elements in the member, respectively.
Table 3: Properties of simulation cases. Name* Main Brace
(in x in) Length (in) Controlling Section (in x in) Friction Coefficient Gap (in) Thickness ratio SR Square HSS6x6x3/8 113.63
Conventional Buckling Brace
SR1A HSS10x0.625 30 % 0.1765 1.67 SR1B HSS10x0.625 10 % 0.1765 1.67 SR2A HSS9.625x0.5 30 % 0.105 1.33 SR2B HSS9.625x0.5 10 % 0.105 1.33 RS Round HSS7.5x0.375 113.63
Conventional Buckling Brace
RS1A HSS8x8x1/4 30 % 0.017 0.67 RS1B HSS8x8x1/4 10 % 0.017 0.67 RS2A HSS8x8x1/8 30 % 0.134 0.33 RS2B HSS8x8x1/8 10 % 0.134 0.33 RS3A HSS8x8x3/16 30 % 0.076 0.5 RS3B HSS8x8x3/16 10 % 0.076 0.5 RS4A HSS9x9x5/8 30% 0.169 1.67 RS4B HSS9x9x5/8 10% 0.169 1.67
*SR: Square-in-round tube. RS: Round-in-square tube.
Table 4: Nominal material properties. Fy (𝑘𝑠𝑖) Fu (𝑘𝑠𝑖)
Square Tubes 46 58 Round Tubes 42 58 Plates 36 58
3.2.2. Results of SR and RS simulation groups
Simulation results of the first simulation group (square-in-round) are presented in terms of axial load-deformation relationships as well as deformed shapes, along with relative stress distributions. Figure 26 and Figure 27 present the axial force versus axial displacement of square-in-round (SR) models, and the comparison between the deformed shapes of the conventional brace (without an encasing tube) and a typical SR type TinT-BCB, respectively.
Global buckling of the conventional brace took place at an equivalent story drift ratio (drift angle) of about 0.25% when the compressive strength was 65% of the yielding strength. Following global buckling, the conventional brace experienced local buckling (Figure 27c) and gradually lost 65% of its compressive strength capacity, as indicated in Figure 26. TinT-BCBs, on the other hand, never buckled in the traditional manner throughout the analysis. As shown in Figure 26, the first contact between the two tubes was observed soon after 0.25% story drift ratio (SDR) was reached, resulting in stiffness reduction. It should be noted that the slight difference between SR1 and SR2 specimens (Figure 26) in terms of the stiffness change was due to variation in gap amplitudes. Subsequent to the first contact between the two tubes, all TinT-BCBs experienced strength degradation before attaining the tensile strength capacity of the inside tube. A strength degradation of about 15% with respect to the tensile capacity occurred in all cases in the SR simulation group after a drop at 0.5% SDR. This can be attributed to the rotation of the brace end, as illustrated in Figure 27b. Although the outer tubes controlled the global buckling of the main braces until a certain deformation level, the main brace eventually suffered local plastic deformations (Figure 27d) through the initiation of global instability (Figure 27b). Note that the gusset plates were designed to allow out-of-plane rotations, a factor that induced an additional flexural demand on the brace assemblies. As indicated in Figure 26, there was a slight drop in the strength after
formation of the local deformations, and consequently the contact between the tubes became more substantial in the vicinity of the local plastic deformations (Figure 27d), so the compressive strength was increasing for a while after the contact owing to the friction force transfer. It is also noteworthy that neither friction coefficient nor the section properties of the buckling-controllers had a significant impact on the behavior of SR cases, since the brace assemblies were not capable of controlling the flexural demand imposed by end rotations.
Figure 26: Axial force vs. axial displacement of SR cases.
a) Global buckling of the conventional brace.
b) Typical deformation of square-in-round BCBs.
c) Sec A-A d) Sec B-B
Figure 27: Deformed shapes of the conventional brace and a typical Square-in-Round TinT-BCB at 4% SDR.
Global buckling of the conventional brace
Brace end rotation initiates
Local deformations of the main brace
A
First contact between the tubes
A
B
Figure 28 and Figure 29 present the axial force versus axial displacement and deformed shapes of RS simulation group, respectively. As expected, the conventional brace buckled globally at about 0.25% SDR and lost 60% of its compression strength when the brace attained an axial deformation quantity corresponding to 4% SDR. The impact of encasing on the brace behavior, however, differed from one case to another based on the properties of the controlling section.
The RS1 and RS3 cases experienced global instability, with the RS3 cases, in particular, exhibiting a trend similar to that of the conventional brace with a larger compressive strength. The behavior of the RS2 and RS4 cases, on the other hand, were governed by local deformation formation, in contrast to the RS1 and RS3 cases. As shown in Figure 28, the strength deterioration became substantial after 1.5% SDR for RS1 and RS2, while the RS4 cases remained stable until an equivalent SDR of 3.5%. Since the outer tube thickness of RS4 was larger than that of the inside tube, local deformations of the inner tube is successfully controlled (Figure 29e) with virtually the same strengths in compression and tension (Figure 28). The deformation pattern shown in Figure 29d demonstrates that the outer tube of RS2 did not effectively control the lateral thrust force imposed by the inner tube. In other words, when end rotations were not substantial, regardless of the gap amplitude and the friction coefficient, the simulation cases with an outer tube thickness less than that of the inside tube were not capable of controlling formation of local deformations in the main brace (Figure 28).
Variations in the friction coefficient did not play an important role on the behavior of the braces when severe local buckling occurred in the members, as observed in RS2 (Figure 29d). However, when the buckling of the inner tube was controlled by the outer tube, the smaller friction coefficient led to less compression overstrength. Even though the difference was not substantial, comparing RS4A with RS4B indicates that the case with a friction coefficient of 0.1 (RS4B)
followed a trend virtually identical to the tensile strength, while the compression strength of RS4A case was slightly larger than the tensile strength.
Figure 28: Axial force vs. axial displacement of RS cases.
a) Conventional brace. b) Typical deformation of round-in-square BCBs.
c) Sec A-A d) Sec B-B in RS2A e) Sec B-B in RS4A. Figure 29: Comparison of deformation of conventional braces and SR-BCBs at 4% SDR.
3.2.2.1. Key observations
Based on the FEA results and deformation patterns obtained from SR and RS simulation groups, the following observations can be made:
A
A
B
i. Similar deformation patterns in terms of the location of the localized plastic deformations were observed in both SR and RS cases. Encasing the conventional braces with an outer tube led the plastic region of the braces to be shifted from the middle portion to the loading end.
ii. The flexural demands imposed by the end rotations, more or less, affected the overall behavior as well as axial force-displacement relationship of the BCBs. It seems that the deformation that initiates end rotations and the severity of the impact were determined by the efficiency of the buckling controllers. Given that both SR and RS simulation groups possess comparable gap amplitudes and relative outer tube thicknesses, the distinction between their behaviors regarding the governing limit states (i.e. global instability or formation of local plastic deformations) can be attributable to the difference between the confinement provided by the circular- and square-shaped buckling controllers.
iii. In contrast to the observed deformation patterns in SR simulation group, the limit states of the TinT-BCBs in RS simulation group were not predominantly governed by global instability due to end rotations. The behavior of the braces in the RS group in certain cases was governed by the inside-tube to outer-tube thickness ratio. The larger the relative outer tube thickness, the less likely strength degradation occurred.
iv. The effect of the coefficient of friction on the force-deformation relationship was not noticeable unless the outer tube successfully controlled the local and global deformations of the inside tube.
3.2.2.2. Impact of enhanced connections
Simulation results presented in the previous section have demonstrated that connection design has a determining impact on brace behavior. Even though utilizing particular parameters successfully prevented BCBs from experiencing global instability (e.g. RS4), in seismic design practice, allowing such rotational demands might not be practical, so in this section an enhanced gusset plate design, presented in Figure 30, has been developed to maximize the effectiveness of BCBs with any design parameters. To investigate the impact of the new gusset plate configuration, the SR2 and RS1 cases, that experienced a significant strength loss in the previous section, are simulated once again with the enhanced connections. In addition to the models that underwent global instability (SR2 and RS1), the gusset connections of RS4, that appeared to be the optimal case among the others, was also enhanced. As shown in Figure 30, the gusset plates were stiffened with four tapered rather than rectangular stiffeners to minimize the additional steel weight as well as to provide a constraint against the end rotations.
All numerical parameters and materials used in this section were identical to those used in the previous cases. A fixed end boundary condition is applied to the stiffeners to represent the constraint provided by the flanges of the beam and the column in an actual structure. Figure 31 shows the FE model of RS1A case after adding both the stiffeners and the applied boundary conditions. Note that RS1A-S accounts for the RS1 model with enhanced connections.
Figure 31: RS1A-S case (RS1A with stiffeners).
Figure 32, Figure 33, and Figure 34 compare the relative efficiencies of the TinT-BCBs with and without stiffeners in terms of axial force-deformation relationships and deformed shapes at 4% SDR. The following can be observed:
i. As can be seen in Figure 32 and Figure 33a, irrespective of cross-sectional shapes, introducing stiffeners to the gusset plates significantly improved the BCB performance in terms of plastic deformation capability without significant strength loss because the limit state that triggers the strength loss was altered with the enhanced connections in both the SR2 and the RS1 cases.
ii. It seems that the level of improvement was more substantial in the SR2 cases than in the RS1 cases. Although both cases attained the same deformation level without
significant strength or stiffness loss, as illustrated in Figure 32 and Figure 33a, the flexural constraint provided by the stiffeners postponed the occurrence of strength loss from 1.5% SDR to 2.5% SDR in the RS1 cases and eliminated the strength loss in the SR2 cases. It should, however, be noted that the difference between the level of enhancements achieved by SR2 and RS1 cases might not be due only to the rotational constraint provided by the stiffeners. In fact, the observed strength deteriorations in RS1 and SR2 cases had two discrete causes:
a) The outer tube thickness in RS1 case was not sufficient to control the lateral expansion of the inside tube, as indicated in Figure 33a. Considering the fact that the lateral thrust force can be associated with the applied axial compressive force and the gap amplitude, the likelihood of premature strength loss for the RS case can be reduced by introducing a thicker outer tube capable of mitigating the severity of the local deformations while resisting the lateral thrust force. Note that the gap amplitude was as small as possible (0.017”) in the RS1 specimen.
b) The strength loss in the SR2 case, conversely, appeared to be more conceptual than the design deficiency observed in the RS1 case. As shown in Figure 32, while the local stiffness provided by the outer tube was sufficient, due to the cross-sectional shape of the two tubes in RS1, the large gap between the flat portions of the square inside tube and the round outer tube allowed the flat portions to deform in a concave manner, a situation that could not be avoided by altering the buckling-controller properties like increasing the outer tube thickness or reducing the initial gap. However, by diminishing the end rotations,
